You will find vociferous advocates for both the Ring of Kerry and the Dingle Peninsula (which includes Slea Head). Both are fantastic. I'm partial to the Ring of Kerry and especially the Ring of Skellig which is the westernmost offshoot of the ROK.
Dingle peninsula has a beautiful drive especially along the southern side w beautiful Inch Beach land the picturesque, though often tourist clogged town of Dingle. Both are beautiful but when we were there in May were tourist heavy. Further west is Slea Head which is a spectacular drive. We loved the small village of Ventry and its beach - that was oddly not as clogged. Nearby Dunbeg Fort was interesting. The drive out Slea Head with its views of the Blasket Islands was absolutely stunning and well worth the whole trip. Here we did run into a lineup of tour buses that made the drive a bit frustrating. We didn't get the chance to take a boat out to the Blaskets but we heard that is fantastic. The drive up north has some great stuff - Ballyferriter which is a nice village, the Gallarus Oratory and more stunning views. There is some gut wrenching driving if you have a fear of heights as I do but it is doable. Stunning scenery - a wonderful drive.
The Ring of Kerry can be tour bus clogged but not in our experience - being there in April, May and September. The south side of the Ring is stunning. The view above Caherdaniel is insanely beautiful, Loher Cashel and Staigue are ringforts that are easy to get to but not at all tourist overrun. Their pure wildness was amazing. Derrynane is wonderful with the Standing stone, the home of Daniel O'Connell. The little village of Sneem was great with beautiful views and fun shops and restaurants. Further on is the larger Kenmare and the gorgeous areas at Killarney National Park which are fantastic w tons of varied things to see.. Killarney itself is SUPER touristy and not my favorite place. The North side of the ROK has great history w two great old ringforts near Caiherseveen, Kells, Rossbeigh beach and great views of the ever present mountains - the Magillicuddy Reeks.
The highlight for us though was Ring of Skellig at the peninsula end. It's real wild Ireland. With the amazing Cliffs of Kerry (far better than the Cliffs of Moher), spectacular breath taking scenery in the Glen, Ballinskellig Beach w the ruins of McCarthy's castle and the Abbey, the wonderful small village of Portmagee with its access by boat of the awe inspiring Skellig Michael, as well as Valentia Island and the wonderful nearby town of Waterville with its great beach, restaurants and Loch Currane NONE of it tourist clogged. The pubs are wonderful peaceful family oriented spots to eat. You can get trad music if you want but none of them overwhelm you with it.
I live in a tourist destination in the US. We tolerate visitors and try and be nice but the folks of Ireland and Kerry in particular are welcoming, warm, funny and above all genuine. We found so many fantastic interactions with the people there it was staggering. Above all give yourselves time for those moments.
So in summary both options are good options. We preferred the ROK because of the Ring of Skellig offshoot and found it calm FAR less touristy and utterly spectacular. You could easily spend 6 days in either place or 3 days in each. Overall we found more variety, more expansive areas w less tourists and a calmer time on the Ring of Kerry and Skellig ...... but the cool thing is you can't go wrong. Give yourself time, don't rat race, linger and interact with the people and it will be a dream come true. Absolutely love Kerry !!!