I invest on TDAmeritrade. My experience so far has been only positive. They don't charge any commissions and your selection of stocks is significantly larger than EE. I have not come across a stock that I couldn't find on TDA.

The drawbacks are threefold from my perspective:

1. Registration process: They still require you to fill in actual forms (I just used a PDF editor instead of printing it out) that then need to be faxed or physically sent by post. This is laughable in the 21st century, so I did some digging and found out that you can call them (for free) via Skype at 800-454-9272 and tell them that you want to register but can't or don't want to use mail/fax. They will then provide you a link to their online portal that you can use to upload the documents. Finally, most of the stuff that must be filled in on the document is quite simple BUT it is important that you fill in the correct withholding tax rate on one of the forms (I can't remember which one exactly). We've got a double tax agreement with the USA to tax dividend withholding tax at 15% - on the form you need to reference paragraph 2(b) of Article 10 in the DTA agreement.
2. Moving funds offshore: For someone with bigger capital amounts, this is not really an issue. But for a small-time investor like me the fees incurred in transferring money offshore can be quite expensive. Standard Bank's Shyft app charges a flat fee of $14 per transfer. So ideally you really want to move at least $1000 or more to make it worth your while. Alternatively you can make use of Wise. They charge significantly less fees on a variable scale. You can Google them if you don't trust me. Anyway, I found that the cheapest way to move amounts smaller than $1k is to 1. Buy $ on the Shyft app and load them to the virtual card. 2. Add your TDA account as beneficiary on Wise and use your Standard Bank Shyft virtual card as payment method to transfer funds to your TDA account.
3. No fractional shares: This is something you really only notice once you don't have it. We are really spoiled with EE allowing you to buy with small amounts. Most ETFs are $100 or more per unit. This makes something like balancing your portfolio tricky with smaller amounts. Luckily you can activate dividend reinvestments which is nice and cost-free. TDA is however merging with Charles Schwab, a broker that allows fractional shares. There is thus a possibility that TDA will soon offer FSRs as well, but the timeline of the merger is not clear. Ironically enough, we can't open an international brokerage account with Charles Schwab, that would've been the easy solution to gaining access to FSRs.

That said, there are multiple other advantages like inter alia being able to set limit orders over EE that is a more vanilla offering. I'd definitely recommend anyone to open an account with TDA and experience it for themselves.