A bit more info is required .
What does the 'summer' setup consist of? speakers, sources etc?
what will be the main use of the amp - music, tv or both?
The key difference is one is a AVR and the other is a stereo amp and typically, a AVR will cost on avg 3x the cost of a equivalent performing stereo amp.
Arcams AVRs are known to have very good stereo performance in term for music, especially their higher classed AVRs . Not sure how the Alpha 10 and the AVR250 compare in that but If music is the main priority then the alpha 10 is my thinking. However if you are happy with the 250 stereo performance , then the 250 (due to it available digital inputs, which most tv's audio output are and other possible devices), is probably the one to look at.
But you will only know what is what once you hear them. All other answers, including my own, are just opinions, as said by Larkone, but it does help to know what they will be working with and the main use of it