Without doubt a civil war, possibly fuelled by the Spanish and French supporting the Catholics, the Puritans uniting with the Anglicans and Presbyterians to eventually prevail. The Dutch would probably get involved too. This would basically replace the Anglo-Spanish war and as far as I can tell it could go either way.
Certainly no English settlement of the American eastern seaboard, instead the Dutch get more room. They would probably not get on with the Catholic French, settlement probably still fairly localised. North America divided between French and Spanish interests and intermittent war on the plains for two centuries.
If the Protestants win the war in England then probable establishment of a Cromwell-type state in the 1610-20s. Catholic pogroms and emigration from England to Ireland and Catholic New France by the 1630s if this isn't too early to support them.
Personal union is off the cards as long as the Puritan state is around. If the monarchy is restored in mid-century it will not be Catholic. There's no wealth coming to England from America and the French and Spanish still have enough room over there for a few decades of peace so the buggers are going to try and invade us when we are at our weakest. The Puritans will fall one way or the other and we will probably have to go cap in hand to the Dutch and they might send over a William 50 years early.
If we somehow survive intact, a moderate William-type Protestant/parliamentary monarchy would arise and eventually unite with Scotland, and maybe even with the Dutch in a much stronger personal union if we're in a really bad way, but Scottish union would have to wait till a king could be found to do a personal union and then wait at least 50 years for full union - no Acts of Union before 1750 if we're very optimistic.
The Scots would probably have primacy within the union too.
The French would doubtless rule America and the world today, I think they'd probably beat the Spanish by the time they ran out of land and had to have a war. For England's and Protestantism's sake we would have to hope that was sooner rather than later.
I don't think the world would be as developed or democratic as it is today due to the decimation of Protestant power, it was no fun whatsoever but it was a more clear-thinking, revolutionary, science and technology-friendly ideology at the time.
The only way for Guy Fawkes to be successful and England/Britain to still become a world power is if by chance some Anglican royal survives and is chosen who can unite the English and the Scots under a personal union as quickly as possible and slash and burn the Catholics before France and Spain can react.