Several notable differences between the 2960 and 3560-E; the former is L2 only, the latter supports L3. The former doesn't support 10 gig, the latter does. The former generally always doesn't guarantee either wire-speed forwarding PPS or internal bandwidth for all the ports, the latter comes very, very close. The former includes limited lifetime hardware warranty and free software updates, the latter, you'll need to purchase maintenance if you want coverage of the hardware and/or software.

The 3560-E is a much feature richer platform in many aspects vs. the 2960, but it's these features that adds so much to the unit cost. If it's just a question of POE power budget, and you're unable to use power injectors, and the additional (expensive) features aren't useful to you, you might consider buying more of the less expensive series switches with POE and perhaps not utilize all their ports.

PS:

BTW, you might also want to look at the stackable series switches, for instance the 2975 and 3750 series.

PPS:

Is the vendor making this recommendation also selling you the equipment?

The 3560E support enhanced PoE (aka PoE+) of up to 20 watts per port. The 2960 PoE will only support up to 15.4 watts. You may need PoE+ to support 1250 with both radios operational. (Take note the emphasis on the word "may".)

HOWEVER, if you upgrade your firmware, for Autonomous IOS its 12.4(10b)JDA3 and for LWAP the firmware should be 5.0.173, the 1250 should be able to operate at 15.4 watts with both radios operational at the cost of lower MCS rates.

I know what I am talking because that's what we are using right now.

Hope this helps.

You have to understand that 1140 and 1250 have GigabitEthernet interface. So it's worthwhile to have the AP's connected to a Gig interface too otherwise anything less than a Gig will be a cause for bottleneck with your Wireless network.