What do I find tricky about the clarinet?

Yes, I'm sure it is - all these things are a bit subjective, but almost everything I've ever read takes that point of view, and having tried both, I agree with it. 

It makes sense that it should be so, I think.  The clarinet has evolved in a relatively hotchpotch manner over a couple of centuries (albeit that Klosé made major changes that have remained largely unaltered since) whereas the sax was "invented" by an expert in instrument technology.  It overblows an octave which makes the fingering much easier.  It has no open tone holes: not only are these easier to play (I know you have a plateau clarinet) but holes can be positioned and sized primarily for acoustic reasons without worrying too much about whether they can be reached and covered by a finger.  They have automatic octave keys that change the position of the vent hole according to what part of the register you are in which improves intonation - the instrument does it for you.  Because of overblowing an octave, there are no "throat notes" needed to bridge the gap, so you don't need to work on improving their often patchy tone; it's also easier to jump from lower to upper register because the jump is smaller - B♭ to C is a horrible jump on the clarinet.  Because of the full mechanism there is no note like that notorious B♭ that uses the register vent as a tone hole.  It's even easier to look after because it's metal, not wood.

It still uses reeds, so you have to deal with those either way.  It's also a transposing instrument.  I think the clarinet has a nicer sound, but that really is subjective.

I think the main drawback is the weight, they really are much heavier than a clarinet.  However, that is slightly offset by the shape which means that you can support the sax with a sling that puts the keys under your fingertips while at the same time putting the mouthpiece in a good position to blow into.  I have personally found that a sling with a clarinet does one or the other but not both.

If you are seriously considering a bit of experimenting - and why not! - the most obvious choice might look like soprano because it's smallest and lightest and most like a clarinet.  However, it's not the easiest to play.  Alto is probably the best place to start.  Because they are so widely played they are available for very reasonable prices - Thomann do a cool-looking black one for €400 but you can get good quality 2nd hand instruments easily.  There's loads of support, online resources, etc, for all kinds of saxophone.  Lots of places sell and service them.