This seems to be such a gray area. It seems to me that we don't know that "he was more severe on his daughters" or severe on any of them at all.

And as far as harsh words, the harshest thing I can think of him saying was to Fanny ch.3. I hope you may be able to convince him that the many years which have passed since you parted have not been spent on your side entirely without improvement; though, I fear, he must find his sister at sixteen in some respects too much like his sister at ten.

It was very insensitive of him to say and badly done, so I'm not defending it.

When Tom's behavior called for harsh words, all Sir Thomas said was this ch.3 “I blush for you, Tom,” said he, in his most dignified manner; “I blush for the expedient which I am driven on, and I trust I may pity your feelings as a brother on the occasion. You have robbed Edmund for ten, twenty, thirty years, perhaps for life, of more than half the income which ought to be his. ...

In Ch 2, when Fanny arrived Sir Thomas, seeing how much she needed encouragement, tried to be all that was conciliating: but he had to work against a most untoward gravity of deportment; and Lady Bertram, without taking half so much trouble, or speaking one word where he spoke ten, by the mere aid of a good–humoured smile, became immediately the less awful character of the two.

Robbin quoted from ch 3. he had never seemed the friend of their pleasures. That paragraph goes on to say...and without aiming at one gratification that would probably have been forbidden by Sir Thomas, they felt themselves immediately at their own disposal, and to have every indulgence within their reach.
We don't know what types of activities were forbidden, but that the girls perception of freedom increased without even aiming at anything forbidden.

It seems more like his natural gravity of deportment and serious nature caused them all to be in awe of him, so it naturally made everyone more serious in his presence. Just guessing here, but it doesn't seem like he was very affectionate, but neither does it seem that he forced the girls to just sit and look pretty on the couch.

It's interesting that the two bad adaptations of MP have Sir Thomas yelling (at a rambunctious Fanny no less) when the text doesn't seem to back that up.