The Indult-SSPX disagreement is a bit like the SSPX-sede disagreement.
Leaving aside other things for now, so far as this thread topic is concerned, in offering the Mass, the difference lies essentially and ultimately in how highly one prizes independence from Rome and the degree of separation from it one deems desirable as such, since this is considered indispensable to growth and freedom - but to take two extreme examples, there were two groups that went different ways from the SSPX - the SSPV and the FSSP - St.Peter's now after about 20 years has over 200 priests and 150 seminarians, without the benefits of independence, has not constantly divided further etc - how does the SSPV compare? Go ahead and down thumb me some more, but the point remains independence is no panacea. Sure, the SSPX is in a league of its own, but the FSSP is easily next best by far.
Summorum Pontificuм will not make the problems in the Church go away overnight, especially with a hierarchy that at large is still at best indifferent to tradition, but it can definitely prove to be a game-changer in the long run, and a stepping stone to better things, like a universal restoration of the Tridentine Mass, since current and future seminarians will learn to offer the traditional Mass. I don't agree with the poster above who claimed Archbishop "Lefebvre set back the Universal Indult by 20 years" but I do think the Indult groups have played an indispensable role in making the Mass available and accessible to the wider Catholic faithful and ultimately in the grant of the "universal indult". Bishop Fellay has admitted this, and, to another poster above, it was indeed Bishop Fellay who specifically requested the same of the Pope along with the other SSPX Bishops.
I suppose it varies from place to place - but many priests of St.Peter's are not hostile to the Society and in fact, with some exceptions, frequently recommend it - the canonical irregularity is a trifle to them. But their approach differs with the Society in that working under a regular canonical structure, despite its difficulties, introduces the possibility of having a wider sphere of influence and a broader apostolate. To most lay Catholics, "irregularity" with Rome is a huge deal - and these souls would never have known or forever have stayed away from the TLM if not for St.Peter's and similar Indult groups.