I'm dealing with US and UK infantry in completely different way. I find their M1s and Enfields deadly at 200 meters distance, I try to engage them at close range with my Jäger troops.

Yes, that works. But only if you use Jager or sturm or any other special squad and as I said its just as good as Tiger only battle (at least for me). This leads my to one think- I have no problem with Fallschimjagers, Granadiers etc. they can be set to QB, it just seems like some important defensive position or Panzer-Panzergranadier division breaking thru lines, so its OK but this squads still have K98 as main weapon. Generally is the situation better on the end of the WWII- "better" infantry squads (like Fallschimjagers, SS units, granadiers) have more MP44 which add them some more firepower on 200 meters then K98 did. On the other hand yenkees have 1 extra BAR in 45 so its actually not so nice.
The added firepower in Granadier and Fallschimjager squads usually comes from 1 extra LMG :) so its still better to keep distance and use them as support, specialy because those units are expensive.

Btw: does anyone know if type of infantry have anything to do with morale? SS units should have much better morale then standard infantry, even if both are regulars, but in game it just does not seem to be this way

Yea, Garands are better than Mausers but German infantry has more SMGs and better MGs.

I don't think that the type of infantry has anything to do with the morale, but some of the guys here say so.

Type of infantry has nothing to do with morale....if you think all SS troops should be veteran or crack, then buy them as veteran or crack and pay the extra cost. You can see from the purchase screens that the SS cost the same as an equivalent Heer unit at the same morale level....if they were better, they'd cost more.