The differences are detailed at
http://www.altera.com/products/software/products/quartus2web/features/sof-quarweb_features.html In short,
- To use Logiclock and Logicprobe in the web edition you must turn on talkback.
- The web edition is missing the IPS-BASE suite of IP cores, the FIFO Partitioner megacore, LogicLock, the incremental flow, Hardcopy, and high-end parts
For the Modelsim AE (or "Altera Edition", which is free for a limited time) there is a slow-down loop that kicks in once your design passes an unspecified threshold, however it will still compile. Also, some of the advanced diagnostic modules present in Modelsim SE (the full-blown product as purchased from Mentor) are disabled or missing in Modelsim AE. Modelsim AE is also a single language simulator, requiring you to specify either Verilog or VHDL when you initially order a license.