Beam is being released tomorrow, but Grin has not yet. What are the main differences from these 2 mimblewimble implementations?
Given the alleged goal of creating a politically independent means of value exchange, the fundamental differences between the projects are extremely dramatic.
Grin has no investors, and every aspect of its development is voluntary, from the mathematics to the aesthetics. There is one paid developer who volunteered for the project and subsequently the community has raised money through donations to pay for him to continue to work full time on the project . There is no incentive to donate to grin except to see the project continue to be developed. The grin community skews toward idealistic/cynical, paranoid, inspired cypherpunk types. Grin is a bonafide ad-hocracy. No one can get grin coins without mining or trading them; there is no premine, presale, ico, instamine or anything else of the sort [1.5]. The core developers of grin have no advantage over anyone else for getting grin coins. It's nobody's business why they are doing it, but as far as anyone can tell it's not for a quick buck.
On the other hand...
Beam pre-sold an unknown amount of tokens for an unknown amount of millions of dollars to investors in a private ICO. Unfortunately a source for this is difficult to find, because BEAM specifically does not mention any details anywhere on their site about this private ICO; we can only speculate as to why they feel the need to be opaque. If you email them or ask their team members on twiter or telegram however if they pre-sold tokens to investors, they will tell you they did.
BEAM is a for-profit tech company that exists to enrich its shareholders, team members, investors and/or whoever stands to be enriched (they are not required to share this information). Beam for this reason has full-time, paid developers, marketers, advisors. CEOs, CTOs, CFOs and the rest of the heavy bureaucracy needed to get rich as quickly as possible are the key community members of BEAM [1.6125]. BEAM literally solicits people to become "ambassadors" to help simulate a community [1.725].
Beam has less interest than grin, for these reasons, in being "fair." In fact being fair is almost entirely antithetical to the goals of for-profit company, profit being specifically to make money at another's expense. At launch BEAM blocks were being mined every second, heavily enriching early miners. One of the core advisors to beam, a man named guy corem, is also the owner of an ASIC development company : Guy is in a position to enrich himself twice, once from selling BEAM tokens allotted to him by the 20% centralized tax taken from miners securing the network, and again by using insider information to develop secret (and/or public) ASICs to mine BEAM at a severe advantage .
People who overlook the delicate premise of a truly sovreign currency, and misunderstand how neutral and transparent the actual mechanics of such a network must be to even begin to be viable, can see that BEAM has a lot of things working against it to ever be useful.
Bitcoin came around to programatically and transparently remove the need for a "Federal Reserve" and provide the method for indepentent power/organization enough to maintain a high value, public ledger. BEAM appears to just be replacing the Fed with their own 20% tax and oversight. It is absurd if you imagined some central entity taking 20% of every single dollar in the entire economy and using it to pay a group of profit-oriented early investors (and of course, to maintain its own power). There is no oversight whatsoever except what BEAM says. If you ask about their transparency they will remind you that, of course, their code is "open-source (TM)" (except the wallet update they released right after they rushed to launch their mainnet, albeit for understandable reasonings.) [3.333333]
At the end of the day the people you have to trust to use grin have less power over the network than the ones you have to trust to use BEAM. This is the most important distinction for me personally.
[1.6125] They have hilarious twitter handles too. I haven't looked into where they got these people. https://twitter.com/BeamCTO
 There is no evidence except thousands of years of human nature that Guy is already planning to do this (well that and the bare evidence that he runs a cryptocurrency ASIC company and is a lead advisor and insider to a for-profit cryptocurrency). That he is in a position to become corrupted by greed is dangerous enough given overarching premises we're dealing with. There is of course a chance Guy is a one in a trillion saint beyond human temptation, but then, why does he spend so much time on twitter?
The only detailed comparison I could find was this: https://tlu.tarilabs.com/protocols/grin-beam-comparison/MainReport.html
which is, if summarized (by a computer):
- In summary, Grin and BEAM are two open-source projects that are implementing the Mimblewimble block chain scheme. Each project does contain some unique functionality but as Grin's goal is produce a minimalistic implementation of Mimblewimble the majority of the unique features that extend Mimblewimble lie in the BEAM project.
- Grin uses a Directed Acyclic Graph (DAG) to represent their mempool to avoid transaction reference loops  while BEAM uses a multiset key-value data structure with logic to enable some of their extended features .
- Andrew Poelstra published a follow-up paper that addresses many of these issues and refines the core concepts of Mimblewimble  which have been applied to the practical implementations of this protocol in both the Grin  and BEAM  projects.
- Grin is aiming to be a simple and minimal reference implementation of a Mimblewimble block chain so they are not aiming to include many features extending the core Mimblewimble functionality as discussed.
- BEAM also supports the traditional timelock feature but includes the ability to also specify an upper time limit after which the transaction can no longer be included in a block .
- BEAM has not specified their mining reward or fees structure as yet but based on their current documentation Grin is planning on a 60 Grin per block reward.
- Grin and BEAM are two open-source cryptocurrency projects based on the Mimblewimble protocol.
- Grin's implementation allows for transaction aggregation and cut-through in the stem phase of propagation which provides even greater anonymity to the transactions before they spread during the fluff phase .
- Both Grin and BEAM have incorporated a version of the Dandelion relay protocol that supports transaction aggregation. In addition to the secure BBS communication channel BEAM also supports one-sided transactions where the payee in a transaction who expects to be paid a certain amount can construct their half of the transaction and send this half constructed transaction to the payer.
- Requiring the interactive participation of both parties in constructing a transaction can be a point of friction in using a Mimblewimble block chain.
- BEAM solves this problem by using a process they call kernel fusion whereby a kernel can include a reference to another kernel so that it is only valid if both kernels are present in the transaction.
- Grin and BEAM both implement the Mimblewimble protocol but each has been built from scratch.
- BEAM has proposed a scheme to reuse these transaction kernels to validate subsequent transactions .
- In order to consume the existing kernels without compromising the transaction irreversibility principle BEAM proposes using a multiplier to be applied to an old kernel, by the same user who has visibility of the old kernel, to be used in a new transaction.
- BEAM's implementation however contains a number of modifications to the Mimblewimble approach with the aim to provide some unique features for their implementation.
- The Mimblewimble protocol describes how transacting parties will interactively work to build a valid transaction using their public/private key pairs, used to prove ownership of transaction outputs, and interactively chosen blinding factors.
- This article provided the basis for a new way to construct block chain style transactions that provided inherent privacy and the ability to dramatically reduce the size of the block chain by compressing the transaction history of the chain.