FutureCaptainB738, Seat62k is right and I apologise. While I'm in MAD every month, haven't used T4 in about 2 years, and back then the metro still hadn't been extended, but I see it now goes from T2 to Barajas (the town where the airport is located) and then onto it's last stop at T4.
However, Given the walk from the metro in T2 to T1 (at least U2 desks are in first bunch as you enter T1 from T2), I think the journey travel time will be more or less the same. From the airport page, when checking on how to transit between terminals, they only refer to the transit shuttle bus, and not the Metro, while it is a viable possibility. I also see you have to pay to use the metro (obvious) but they also mention of a supplement of €1 to enter and to exit metro between terminals???
Regarding taxis, does that work well. MAD attracts, often, the worst of taxi drivers in Madrid. They often refuse to do short trips, often take tours, and the people controlling them onsite are usually awful. Lines for taxis can often be slow. My advice is if you arrive into T1 ontime, dash off the plane first (passport control in T1 is usually painless and swift, unless numerous flights arrive at same time from non Schengen countries, and if luggage comes out quickly, and you RUN I think you MIGHT just make it, but luck would really need to be on your side. Whether metro or bus, it's a toss of a coin. Personnally, I'd go for bus, as straight out of luggage claim you just exit terminal and the bus is there. To get metro you have to go upstairs in T1, walk the length of most of T1 (check-in area often crowded, or quite, rarely in between in my experience), then head down connection to T2 following METRO signs. Buy metro ticket, etc. Writing all this makes me think the transit bus is the best option.
Good luck or buena suerte as they say in Spain!