Air Carrier Captain reported an obstacle warning during approach. Crew executed a missed approach and returned for another landing without incident.

Narrative

On vectors for the 4L visual approach backed up with the rnav (gps) 4L into BTR; ATC advised of Aircraft Y traffic just outside the final approach fix (GOCET) at 3000 ft. Aircraft Y was instructed to climb to 3;500 and we were instructed to descend to 2;000 and assigned a heading inside the FAF. Upon reaching 2000 ft we were told descend to 1800ft and cleared for the visual approach. The minimum altitude at GOCET is 2000 ft so we knew capturing past GOCET and at 1800ft could leave us high. We were already gear down and flaps 30 before capturing the inbound course. The FO called for flaps 45 before landing checklist as we captured the inbound course and we were alts cap at 1800ft. I noticed that we lost the vertical guidance and flying level at 1800 past GOCET I told the FO to start descending. The FO turned off the auto pilot and continued the turn to final. I tried reloading the approach to get the vertical guidance back but it kicked it out shortly after executing. As we rolled out on the approach course I noticed we were a little low for the runway but correctable; however there are some antennas on short final for 4L at 472 ft and there is no visual vertical guidance for that runway. The FO continued descending and mentioned that we were still above 1000ft and it occurred to me that the FO might have thought the snowflake was below us and he was trying to descend to capture it. It was at about this time that we received an Enhanced Ground Proximity Warning System (egwps) caution obstacle. I told the FO to stop descending and the FO acknowledged it was going off for the antennas in front of us. The antennas were insight the whole time so the FO continued to attempt to climb to get back on path and clear the egpws caution. However; we then received the egpws obstacle pull up alert and the FO stated go around. I confirmed go around and the egpws alert went away almost immediately since we were already climbing. The FO used TOGA thrust since the obstacle was in sight and we were visual and cleared the alert right after executing. We executed the go around procedure and got vectored back around for the approach outside the FAF where we captured the course and glide path. We landed without further incident. Upon reaching the gate the FO sent an acars message to dispatch and maintenance notifying them of the go around and I called both dispatch and maintenance before we left to confirm they received it.Cause: 'Aircraft Y traffic off our right and just outside the FAF caused us to accept a turn inbound tighter than usual combined with an already low altitude of 1800 ft to intercept the approach. We were aware the runway did not have visual vertical guidance but we were not expecting to lose the rnav vertical guidance as well; forcing the FO to fly completely visual. This combined with the antennas off of runway 4L and miscommunication on why we lost the glide path resulted in us being low on the approach and receiving an egpws alert and executing a go around.'Suggestion: 'Instead of accepting the turn inbound for the approach we could have asked for vectors back around or through the approach course and behind the other traffic to prevent such a short approach to final. After turning final instead of bugging the missed approach altitude we could have referenced the altitude at HOGTO on the LNAV approach and bugged 900 ft (820 at HOGTO) since it is right over the antennas and would have prevented the egwps alert. Ultimately; in an effort to avoid traffic on the approach we accepted a vector and approach clearance that was tight on its own combined with a loss of vertical guidance left us in a situation where even though we were configured and above 1000 ft could have been abandoned sooner or approach not accepted in the first place.'