My husband and I will be in Ireland for two weeks in September We are looking at three days in either Kenmare or Kilarney as a base for daytrips Does anyone have any ideas or recommendations as to which one would be best as a home base?

Kenmare is a better base. Killarney is a city and lots of bustle and people. Kenmare is a quieter town but still great restaurants and music.
You can use Kenmare as a base to explore Killarney Park with Ross Castle, Muckross House and the waterfall and then head south for a day on the Ring of Kerry. Don't bypass the Skellig Ring on ROK - best scenery!

I am going in October and have based myself in Killarney. I thought we could walk to lots of restaurants and pubs at night and not have to drive. This is my first trip so I can't comment on the differences in the towns. Just telling you where I decided to stay.

Both Kenmare and Killarney are towns and both are excellent bases for touring County Kerry. Killarney is a larger town and can be quite busy, particularly in the summer. Both towns are on the Ring of Kerry.
We have been to Ireland several times and have stayed in both towns on more than one occasion. I think it depends on which daytrips you plan. If you want to spend most of your three days at Muckross House, Killarney National Park, the Gap of Dunloe, Ross Castle and the ROK, then I would base in Killarney. If you want to do just one day in Killarney then do ROK and perhaps the Ring of Beara, I would say that Kenmare would be a good base.

Both towns offer a nice assortment of pubs, restaurants, shopping, lodging.

The last time we were in Killarney we have a great stay at Killarney Lodge (the month was April, so more "shoulder" season):
https://killarneylodge.ie/

Our last visit to Kenmare we stayed at Sea Shore Farm Guesthouse (lovely - the month was August, so high season):
https://www.seashorekenmare.com/