TradeStation is a "direct access" broker, and full-feature charting platform. Ameritrade is web-based "retail" broker. You should research the difference between direct access and retail, and whether you need realtime charting capabilities.
I switched from Ameritrade to TradeStation in order to daytrade/scalp stocks. I remember Ameritrade account can be opened for as low as $2K, but for TradeStation you need at least $25K to meet PDT (Pattern Day Trader) requirement. TradeStation website indicated $30K to open equities account, but I started trading with $27K funds.
TradeStation has other features which you are checking from the website. I now use Ameritrade for swing positions, and TradeStation for intraday scalps and swings.
Other similar full-feature broker/platforms use RealTick software (nicer looking charts; built-in scanners) which you should also research. Some traders use e-Signals charting software together with InteractiveBrokers account. InteractiveBrokers' cheaper commissions is half of TradeStation. There is also ThinkorSwim broker.
If you decide on TradeStation, you will find the new Simulator mode useful for training in all four instruments: equities/futures/options/forex. Better than papertrading when you can trade on Simulator mode during live hours using fake $100K account and watch your P&L and trade management statistics.
Use Ameritrade if you have smaller account and trade less often as in swing or longterm. Use TradeStation if you are ready for $25K account and want to trade intraday between 4 to 50 times daily. My Ameritrade swing account is used with free QuoteTracker realtime charting on separate PC.
Regards,