I tend to be mainly a strummer, although for songs where a more delicate touch is required I do use a fingerpicking accompaniment - although not a standard alternating thumb-and-fingers clawhammer style - more arpeggiated!
I've never really been able to master the plectrum/third and fourth fingers style that's used by so many pros so if the style of the song changes midway through, there's a cumbersome drop the pick or pick up the pick moment!
My strumming style is mainly very full and chunky, and (especially if playing alone) I will sometimes throw in a bit of syncopation and occasionally shifting the accents in the bar to try to chuck a bit of emphasis in here and there. I love flowing bass lines, and try to throw those in where the chords allow it to be done,
So, how do you play? :-D
I pick with my nails. Trouble is I've lost a big chunk out of the nail on the second finger of my right hand permanently.
Both, whatever is required. I have to say, few people are able to truly strum a guitar well as a rhythm guitarist. So your last paragraph is exactly to point. When I pick live or while singing, it's flat picking. I finger pick when playing a solo song.
To your paragraph about pick / third and fourth finger style, it was my first picking method. After I learned classical and transitioned into true ringer picking, I lost that ability. However, I still haven't learned true clawhammer style, only travis picking style.
It depends on the instrument and also the role I'm playing in the music. Bass is my main thing and, in my current church playing context, I play with my fingers and rarely strum. In my previous church we had a smaller band and there I would often strum on chords higher up the neck to give a fuller sound, particularly when starting off a song and needing to establish harmony and rhythm. In my current church I also get to play electric guitar sometimes; for that, I almost always use a plectrum and am more likely to be strumming (although the electric guitar generally plays the role of providing funky "icing" rather than the heart of the rhythm).
Definitely a strummer by trade - I whack out some pretty interesting rhythms and muted chords when I get going - but will pick on occasion. The main way I learned picking so many years ago was by listening to my hero, Randy Stonehill (no Youtube back then, only those round vinyl discs...). I just loved the way he played a combination of everything, especially when you saw him live.
I envy guys that can do the plectrum/third and fourth finger style.
Saw Doyle Dykes finger pick a guitar for the first time in November at CMS Northwest. Wow! Just blows me away.